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Killing tensor
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<p>In mathematics, a Killing tensor or Killing tensor field is a generalization of a <a href="/facts/Killing_vector/Ane9xIdV">Killing vector</a>, for <a href="/facts/Symmetric_tensor/CWKBfgnv">symmetric</a> <a href="/facts/Tensor_field/cAC6F6rF">tensor fields</a> instead of just <a href="/facts/Vector_field/ccFNuPPp">vector fields</a>. It is a concept in <a href="/facts/Riemannian_geometry/pPEzjyQC">Riemannian</a> and <a href="/facts/Pseudo-Riemannian_geometry/VFXsVjqb">pseudo-Riemannian geometry</a>, and is mainly used in the theory of <a href="/facts/General_relativity/jVsoIg8X">general relativity</a>. Killing tensors satisfy an equation similar to Killing's equation for Killing vectors. Like Killing vectors, every Killing tensor corresponds to a quantity which is conserved along <a href="/facts/Geodesic/fbWR6l80">geodesics</a>. However, unlike Killing vectors, which are associated with symmetries (<a href="/facts/Isometries/K5wX8ah6">isometries</a>) of a <a href="/facts/Pseudo-Riemannian_manifold/VFXsVjqb">manifold</a>, Killing tensors generally lack such a direct geometric interpretation. Killing tensors are named after <a href="/facts/Wilhelm_Killing/W27PB2MJ">Wilhelm Killing</a>. </p>